A coding scheme for m-out-of-n codes

Ramabadran, Tenkasi V.

doi:10.1109/26.58748

“…The enumeration scheme (h ≤δ , h −1 ≤δ ) can be implemented with computational complexity polynomial in n by methods such as [4, pp. 27-30], [25], [30].…”

Section: A Constant-weight Weak Wom Schemes From Concentrated-weightmentioning

confidence: 99%

Rank-modulation rewriting codes for flash memories

Gad

¹

,

Yaakobi

²

,

Jiang

³

et al. 2013

2013 IEEE International Symposium on Information Theory

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The current flash memory technology focuses on the cost minimization of its static storage capacity. However, the resulting approach supports a relatively small number of program-erase cycles. This technology is effective for consumer devices (e.g., smartphones and cameras) where the number of program-erase cycles is small. However, it is not economical for enterprise storage systems that require a large number of lifetime writes.The proposed approach in this paper for alleviating this problem consists of the efficient integration of two key ideas: (i) improving reliability and endurance by representing the information using relative values via the rank modulation scheme and (ii) increasing the overall (lifetime) capacity of the flash device via rewriting codes, namely, performing multiple writes per cell before erasure.This paper presents a new coding scheme that combines rank-modulation with rewriting. The key benefits of the new scheme include: (i) the ability to store close to 2 bits per cell on each write with minimal impact on the lifetime of the memory, and (ii) efficient encoding and decoding algorithms that make use of capacity-achieving write-once-memory (WOM) codes that were proposed recently.

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“…The implementation of such a coder can also run into problems with very long registers, but elegant finite-length implementations are known and are widely used (Witten, Neal and Cleary [30]). For constant-weight codes, the idea is to reverse the roles of encoder and decoder, i.e., to use an arithmetic decoder as an encoder and an arithmetic encoder as a constant-weight decoder (Ramabadran [16]). Ramabadran gives an efficient algorithm based on an adaptive probability model, in the sense that the probability that the incoming bit is a depends on the number of 's that have already occurred.…”

Section: Definitionmentioning

confidence: 99%

“…Compared to a linear-time encoding algorithm [16], the algorithm presented here is faster only when , in which case the rate of the resulting code, , approaches zero as . However, we view this paper as the starting point of a new approach to the classic problem of encoding and decoding constant-weight codes, and we believe there is considerable room for improvement.…”

Section: Introductionmentioning

confidence: 99%

A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections

Tian

¹

,

Vaishampayan

²

,

Sloane

³

2009

IEEE Trans. Inform. Theory

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Abstract-We present a novel technique for encoding and decoding constant weight binary vectors that uses a geometric interpretation of the codebook. Our technique is based on embedding the codebook in a Euclidean space of dimension equal to the weight of the code. The encoder and decoder mappings are then interpreted as a bijection between a certain hyper-rectangle and a polytope in this Euclidean space. An inductive dissection algorithm is developed for constructing such a bijection. We prove that the algorithm is correct and then analyze its complexity. The complexity depends on the weight of the vector, rather than on the block length as in other algorithms. This approach is advantageous when the weight is smaller than the square root of the block length.

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“…The enumeration scheme (h ≤δ , h −1 ≤δ ) can be implemented with computational complexity polynomial in n by methods such as [4, pp. 27-30], [23], [27].…”

Section: A Constant-weight Weak Wom Schemes From Concentrated-weightmentioning

confidence: 99%

Rank-Modulation Rewrite Coding for Flash Memories

Gad

¹

,

Yaakobi

²

,

Jiang

³

et al. 2015

IEEE Trans. Inform. Theory

3

0

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The current flash memory technology focuses on the cost minimization of its static storage capacity. However, the resulting approach supports a relatively small number of program-erase cycles. This technology is effective for consumer devices (e.g., smartphones and cameras) where the number of program-erase cycles is small. However, it is not economical for enterprise storage systems that require a large number of lifetime writes.The proposed approach in this paper for alleviating this problem consists of the efficient integration of two key ideas: (i) improving reliability and endurance by representing the information using relative values via the rank modulation scheme and (ii) increasing the overall (lifetime) capacity of the flash device via rewriting codes, namely, performing multiple writes per cell before erasure.This paper presents a new coding scheme that combines rank-modulation with rewriting. The key benefits of the new scheme include: (i) the ability to store close to 2 bits per cell on each write with minimal impact on the lifetime of the memory, and (ii) efficient encoding and decoding algorithms that make use of capacity-achieving write-once-memory (WOM) codes that were proposed recently.

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A coding scheme for m-out-of-n codes

Cited by 62 publications

References 15 publications

Rank-modulation rewriting codes for flash memories

Rank-modulation rewriting codes for flash memories

A Coding Algorithm for Constant Weight Vectors: A Geometric Approach Based on Dissections

Rank-Modulation Rewrite Coding for Flash Memories

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